Filtering control method for improving image quality of bi-linear interpolated image

ABSTRACT

The present invention relates to an interpolation method for enlarging a digital image or predicting a moving vector of a compressed image system as a sub-pixel unit when the image digitized through a CCD (Charge Coupled Device) camera ect. has a low resolution in a video phone or video conference or general digital video system, particularly the present invention can be adapted to a post processor of a compressed digital image in order to improve the image quality, and can be used for finding a moving vector of a moving picture compressed type, accordingly the present invention is capable of improving the image quality.

CROSS-REFERENCE TO RELATED APPLICATIONS

More than one reissue application has been filed for the reissue of U.S.Pat. No. RE42,045. The reissue applications are patent application Ser.No. 14/961,306 (present application); Ser. Nos. 14/959,697; 14/961,345;14/959,662; 14/961,275; 14/962,608; 14/962,578; 14/963,765; and14/963,818, all of which are continuation reissues of U.S. Pat. No.RE42,045.

This application is a continuation reissue of U.S. reissue applicationSer. No. 14/472,205, filed on Aug. 28, 2014, now U.S. Pat. No. RE45,859,issued on Jan. 19, 2016, which is a reissue of U.S. Pat. No. RE42,045,issued on Jan. 18, 2011, which is a reissue of U.S. Pat. No. 6,803,954issued Oct. 12, 2004. More than one reissue application has been filedfor the reissue of U.S. Pat. No. 6,803,954. U.S. patent application Ser.No. 11/546,484 is a reissue of U.S. Pat. No. 6,803,954; U.S. patentapplication Ser. No. 12/024,408, now abandoned, is a divisional reissueof U.S. Pat. No. 6,803,954; and U.S. patent application Ser. No.12/424,927 is a continuation reissue of U.S. patent application Ser. No.11/546,484, the entire contents of each are hereby incorporated byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an interpolation method adapted toenlargement of a low resolution image when the image digitized through aCCD (Charged-Coupled Device) has the low resolution, in particular to afiltering control method for improving the image quality of a bi-linearinterpolated image which is capable of restoring a requestedinterpolated high resolution image from a low resolution image byfinding a coefficient of a two-dimensional filter on the basis of aregularization image restoration method.

2. Description of the Prior Art

In the conventional technology, a still picture or a moving picture hasor transmits a low resolution image because it can not physicallysatisfy a sensor having the low resolution or a nyquist value.

In addition, a compressed moving picture has or transmits the lowresolution image due to its bit value problem.

For example, when the compressed moving picture having the low bit valueis transmitted to a receiver and the receiver enlarges the transmittedmoving picture, the resolution of the transmitted moving picture lowersdue to a degradation phenomenon ect.

Accordingly, a method for getting a high resolution image from a lowresolution image is required.

In the meantime, the method for getting the high resolution image fromthe low resolution image is largely divided into an image expansion typemethod and an image enhancement type method.

First, the image expansion type method converts the size of the lowresolution image into a requested size. The bi-linear interpolationmethod, a zero order expansion method, and a cubic spline method arecomprised in the image expansion type method.

However, as described above, the image expansion type method has animage visibility lowering problem because when the image isinterpolation-restored by the above-mentioned method such as thebi-linear interpolation method, zero order hold expansion method, cubicspline method, the outlines of the image is over-blurred.

Meanwhile, the image enhancement type method comprises many methods, butthe image enhancement type method causes a computational complexity,accordingly the method is not suited to a real-time processing due tothe its computational complexity.

In addition, when the image enhancement type method is used for gettingthe high resolution image from the low resolution image, setting of eachparameter is not adaptable.

For example, there is a POCS (Projection Onto Convex Set) method forincreasing the resolution of an image. In the POCS method, in use oftime region information, it is assumed as correlation between the imagesis uniformly same, but actually the correlation between the images isnot uniform.

In addition, there is a mapping method for mapping a non-uniform sampleof the low resolution image into a uniform sample of the high resolutionimage by using moving information and segmentation information of theimage. However, the mapping method has the computational complexityproblem, accordingly the mapping method is not suited to the real-timeimage data processing of the image processing system.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a filtering controlmethod for improving the image quality of a bi-linear interpolated imagewhich is capable of improving the image quality of the interpolatedimage by using an interpolation method considering a real-timeprocessing, a computational complexity and an efficiency when thedigital video system seeks the interpolated image from the lowresolution image.

The other object of the present invention is to provide the filteringcontrol method for improving the image quality of the bi-linearinterpolated image which is capable of finding a two-dimensional filtercoefficient for getting the interpolated image from the low resolutionimage on the basis of a regularization image restoration method.

The other object of the present invention is to provide the filteringcontrol method for improving the image quality of the bi-linearinterpolated image which can approximate and find a PSF (Point SpreadFunction) for the bi-linear interpolated image from a modeling of thedegraded image in the frequency region.

The other object of the present invention is to provide the filteringcontrol method for improving the image quality of the bi-linearinterpolated image which is capable of performing a real-time adaptiveprocessing by finding a filter coefficient from the bi-linearinterpolated image and approximated PSF.

In the present invention, in order to find a filter coefficient forfinding the interpolated image from the low resolution image on thebasis of the regularization image restoration method, when H is the PSF(Point Spread Function), f is a requested high resolution image, Z isthe low resolution image, g is the high resolution image gotten from thebi-linear interpolation method, an added function M (f)=∥g−Hf∥²+α∥Cf ∥²for finding the PSF(H) from an equation g=Bz=Hf+n (B, H are bi-linearinterpolated filters, n is a noise component generated by the assumed H)is defined.

The filtering control method for improving the image quality of thebi-linear interpolated image can be implemented by finding the PSF(H)from the added function M(f) by using an equation

${H\left( {k.\mspace{14mu} l} \right)} = \frac{G\left( {k.\mspace{14mu} l} \right)}{F\left( {k.\mspace{14mu} l} \right)}$

The filtering control method for improving the image quality of thebi-linear interpolated image can be implemented by finding a PSF(P) of af=Pg function by using an equation

${P\left( {k,l} \right)} = \frac{H*\left( {k,l} \right)}{{H*\left( {k,l} \right){H\left( {k,l} \right)}} + {C*\left( {k,l} \right){C\left( {k,l} \right)}}}$after finding the PSF(H).

The filtering control method for improving the image quality of thebi-linear interpolated image can restore the requested high resolutionimage(f) by finding an added filter coefficient Q of the PSF(P) andinterpolation filter B from the equation f=Pg=PBz=Qz.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an image sample for getting a twice enlarged highresolution image according to the embodiment of the present invention.

FIG. 2 illustrates an interpolation filter coefficient for getting thetwice enlarged image according to the embodiment of the presentinvention.

FIG. 3 illustrates an image sample for getting a three times enlargedhigh resolution image according to the other embodiment of the presentinvention.

FIG. 4 illustrates the interpolation filter coefficient for getting thethree times enlarged image according to the other embodiment of thepresent invention.

FIG. 5 illustrates an image sample for getting a six times enlarged highresolution image according to the another embodiment of the presentinvention.

FIG. 6 illustrates the interpolation filter coefficient for getting thesix times enlarged image according to the another embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 illustrates an image sample for getting a twice enlarged highresolution image according to the embodiment of the present invention.

As depicted in FIG. 1, a˜i illustrate low resolution pixels, A˜Dillustrate high resolution pixels. In addition, pixels depicted as ‘x’illustrate pixels interpolated as twice by a twice interpolation filtercoefficient.

FIG. 2 illustrates the interpolation filter coefficient for getting atwice enlarged image according to the embodiment of the presentinvention. In other words, the interpolation filter coefficient forinterpolating the twice enlarged image of FIG. 1 is depicted in FIG. 2.

As depicted in FIG. 2, the high resolution image is gotten from the lowresolution pixels a˜i (3×3 pixels) inside of a circle of FIG. 1 by usingthe interpolation filter coefficient.

FIG. 3 illustrates an image sample for getting a three times enlargedhigh resolution image according to the other embodiment of the presentinvention.

As depicted in FIG. 3, a˜p illustrate the low resolution pixels, A˜Iillustrate the high resolution pixels using the filter according to thepresent invention.

FIG. 4 illustrates the interpolation filter coefficient for getting thethree times enlarged image according to the other embodiment of thepresent invention.

As depicted in FIG. 4, three times enlarged pixels which are newlygenerated illustrated as triangles in FIG. 3 are gotten from the lowresolution pixels a˜p (4×4 pixels) by using the interpolation filtercoefficient of FIG. 4.

FIG. 5 illustrates the image sample for getting a six times enlargedhigh resolution image according to the another embodiment of the presentinvention. In other words, it illustrates the image sample for gettingthe six times enlarged high resolution image from the twice and threetimes interpolation filter coefficients by using the bi-linearinterpolation method.

As depicted in FIG. 5, pixels illustrated as a ‘X’ can be gotten byusing the twice interpolation filter of FIG. 2, and pixels illustratedas a triangle can be gotten by using the three times interpolationfilter coefficient of FIG. 4.

In addition, pixels illustrated as a quadrilateral can be gotten fromthe pixels generated by the twice and three times interpolation filtercoefficients by using the bi-linear interpolation method.

FIG. 6 illustrates the interpolation filter coefficient for getting thesix times enlarged image according to the another embodiment of thepresent invention. In other words, the interpolation filter coefficientfor getting the six times enlarged image of FIG. 5 is depicted in FIG.6.

Meanwhile, as depicted in FIG. 2, FIG. 4 and FIG. 6, the value found byusing the interpolation filter coefficient of the present invention hasan integer value.

In addition, a 9 bit shift is performed to the value calculated by theinterpolation filter coefficient, accordingly there is no need toperform a floating point operation processing.

The twice, three times, six times interpolated images are depicted inFIG. 1˜FIG. 6, however the present invention is not limited by that, itcan be adapted freely to a certain interpolation value.

Hereinafter, the filtering control method for improving the imagequality of the bi-linear interpolated image will be described in moredetail.

First, a spatially invariant PSF (Point Spread Function) for finding theinterpolation filter coefficient according to the each interpolationvalue can be easily analyzed and approximated in the frequency region,accordingly the spatially invariant PSF (Point Spread Function) isconsidered from the bi-linear interpolated image.

After that, when it is assumed as the low resolution image is z, highresolution image gotten by the bi-linear interpolation method is g, highresolution image to be restored is f, the relation between the eachimage can be described as below.g=Bz=Hf+n   [Equation 1]

Herein, the B, H, n are the bi-linear interpolation filters, H is thespatially invariant PSF defining the relation between the original highresolution image and high resolution image gotten by the interpolationmethod, and the n is a noise component generated by the assumed H.

Herein, when the noise component is neglected and a direct inverse isused in order to find the PSF(H), the PSF(H) can be described as belowequation 2 in the frequency region.

$\begin{matrix}{{H\left( {k,l} \right)} = {\frac{G\left( {k,l} \right)}{F\left( {k,l} \right)}.}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

Herein, the H(k,l) is the component in the k,l frequency region of thePSF(H), the G (k,l) is the component in the k,l frequency region of thebi-linear interpolated image. In addition, the F (k,l) is the componentin the k,l frequency region of the high resolution image.

Meanwhile, the high resolution image f to be restored is unknown, thePSF(H) can be gotten from the bi-linear interpolated high resolutionimage through a statistical processing after performing an under-sampleprocessing of various images as various value.

Herein, the high resolution image is gotten by using the PSF(H) foundfrom the direct inverse. In other words, there is a system stabilizationproblem because the high resolution image gotten from the PSF(H) byusing the direct inverse is overshoot in the region where the k,l have‘0’ value (in general, high frequency region) in the frequency region,accordingly the regularization image restoration for improving thesystem stabilization is used to solve the problem.

The regularization image restoration method is used for restoring theimage or finding a certain PSF, an added function M(f) for finding thePSF(H) by using the regularization image restoration method can bedescribed as below equation 3.M(f)=∥g−Hf∥²+α∥Cf∥²   [Equation 3]

Herein, the first term of the right side of Equation 3 illustrates thecredibility of the bi-linear interpolated image, the second term of theright side illustrates increase of the stability of the system byproviding the mitigation to the restored image.

In addition, the ∥.∥ means a norm, the α is a regularization parameterfor determining the credibility and mitigation of the original image. Inaddition, the C is the two-dimensional high frequency filter fordetermining the mitigation of the original image, in the presentinvention a two-dimensional Gaussian filter is used as the C.

When a gradient operator is adapted to Equation 3 in order to get thehigh resolution image, it can be described as below equation 4.□_(f)M(f)=−2H^(T)(g−Hf)+2αC^(T)Cf=0  [Equation 4]

Herein, the T means a transpose of a matrix.

Meanwhile, conventionally a repetition method is used in order to getthe high resolution image and regularization parameter, but it is notsuited to the moving picture processing because the method causes lotsof computational complexity.

Accordingly, in the present invention, the regularization parameter α isfixed as ‘1’, and the high resolution image f can be found as belowequation 5.

$\begin{matrix}{f = {\frac{H^{T}g}{\left( {{H^{T}H} + {C^{T}C}} \right)} = {Pg}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

When the PSF(P) is found by Equation 5. PSF(P)=H/(H^(T)H+C^(T)C)requires the lots of computational complexity for calculating an inversematrix, however the PSF(P) in Equation 5 is a block-circulant matrix,accordingly it can be easily calculated in the frequency region.

Accordingly, the PSF(P) can be found finally as below Equation 6.

$\begin{matrix}{{P\left( {k,l} \right)} = \frac{H*\left( {k,l} \right)}{{H*\left( {k,l} \right){H\left( {k,l} \right)}} + {C*\left( {k,l} \right){C\left( {k,l} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

Herein, the ‘*’ means a complex-conjugate.

The PSF(P) can be found by using an IFT (Inverse Fourier Transform) fromEquation 6.

The requested high resolution image f can be found as below Equation 7by using the found PSF(P) and Equation 1.f=Pg=PBz=Qz   [Equation 7]

The PSF(P) is the spatially invariant function, the bi-linearinterpolation filter B can be easily found by the conventionaltechnology, accordingly the added filter coefficient Q of the PSF(P) andbi-linear interpolation filter B can be found.

Herein, in order to reduce the computational complexity, the number of akernel of the PSF(P) is set in accordance with the up-sampling value.

When the up-sampling value is 2 in the present invention, the number ofthe kernel is limited as 3, when the up-sampling value is 3, the numberof the kernel is limited as 4.

When the up-sampling value is 2, it can be used in an applicationsegment for enlarging the size of the image as twice at a post processorof the compressed digital image and in finding of a sub-pixel movingvector in a H.263 moving picture compressed method.

In addition, when the up-sampling value is 3, it can be used in using ofa ⅓ unit moving vector in a H.26L moving picture compressed method.

Herein, the H.263 and H.26L are moving picture compressed standardspresented in the ITU-T (International TelecommunicationsUnion-Telecommunication).

As described above, the present invention can be used for improving theimage quality at the post processor of the compressed digital image byusing the interpolation method for getting the interpolated highresolution image from the low resolution image when the resolution ofthe digital image lowers due to the low resolution image sensor.

In addition, the interpolation method of the present invention canimprove the image quality by finding the moving vector of the movingpicture compressed type.

What is claimed is:
 1. A filtering control method for improving theimage quality of a bi-linear interpolated image when recovering a highresolution image from a low resolution image, the method comprisingperforming operations using at least one processor, the operationscomprising: restoring a requested high resolution image f by finding anadded filter coefficient Q of a PSF(P) and a bi-linear interpolationfilter B from an equation f=Pg=PBz=Qz, wherein f is the high resolutionimage as requested, P is the PSF (Point Spread Function), g is the highresolution image found by the bi-linear interpolation method, and z isthe low resolution image; wherein the high resolution image f can berestored by performing an added function M(f) definition process forfinding the PSF(H) from an equation g=Bz=Hf+n, wherein B, H arebi-linear interpolation filters, and n is a noise component generated bythe assumed H; and wherein the added function M(f) is defined asM(f)=∥g−Hf∥²+α∥Cf∥², wherein α is a regularization parameter, and C is atwo-dimensional high frequency filter for finding mitigation of theoriginal image.
 2. The filtering control method for improving the imagequality of the bi-linear interpolated image according to claim 1,wherein the regularization parameter α is fixed as ‘1’ in order toreduce a computational complexity.
 3. The filtering control method forimproving image quality of the bi-linear interpolated image according toclaim 1, wherein a two-dimensional gaussian filter is used as thetwo-dimensional high frequency filer C in order to determine themitigation of the original image.
 4. A filtering control method forimproving the image quality of a bi-linear interpolated image whenrecovering a high resolution image from a low resolution image, themethod comprising performing operations using at least one processor,the operations comprising:restoring a requested high resolution image fby finding an added filter coefficient Q of a PSF(P) and a bi-linearinterpolation filter B from an equation f=Pg=PBz=Qz, wherein f is thehigh resolution image as requested, P is the PSF (Point SpreadFunction), g is the high resolution image found by the bi-linearinterpolation method, and z is the low resolution image; wherein thehigh resolution image f can be restored by performing an added functionM(f) definition process for finding the PSF(H) from an equationg=Bz=Hf+n, wherein B, H are bi-linear interpolation filters, and n is anoise component generated by the assumed H; wherein the high resolutionimage f is restored by finding a PSF(P) of a f=Pg function after findingthe PSF(H) from the added function M(f); and wherein the PSF(H) is foundby using an equation${H\left( {k,l} \right)} = {\frac{G\left( {k,l} \right)}{F\left( {k,l} \right)}.}$ G(k,l) is the component in the k,l frequency region of the bi-linearinterpolated image, and F(k,l) is the component in the k,l frequencyregion of the high resolution image.
 5. A filtering control method forimproving the image quality of a bi-linear interpolated image whenrecovering a high resolution image from a low resolution image, themethod comprising performing operations using at least one processor,the operations comprising: restoring a requested high resolution image fby finding an added filter coefficient Q of a PSF(P) and a bi-linearinterpolation filter B from an equation f=Pg=PBz=Qz, wherein f is thehigh resolution image as requested, P is the PSF (Point SpreadFunction), g is the high resolution image found by the bi-linearinterpolation method, and z is the low resolution image; wherein thePSF(P) can be found by getting an IFT (Inverse Fourier Transform) by anequation${P\left( {k,l} \right)} = \frac{H*\left( {k,l} \right)}{{H*\left( {k,l} \right){H\left( {k,l} \right)}} + {C*\left( {k,l} \right){C\left( {k,l} \right)}}}$H(k,l) is a component in the k,l frequency region of the PSF(H), and Cis a two-dimensional high frequency filter.
 6. The filtering controlmethod for improving the image quality of the bi-linear interpolatedimage according to claim 5, wherein the number of a kernal of the PSF(P)is set in accordance with an up-sampling value of the image.
 7. Afiltering control method for improving the image quality of a bi-linearinterpolated image when recovering a high resolution image from a lowresolution image, the method comprising performing operations using atleast one processor the operations comprising: defining an addedfunction M(f) for finding a PSF(H) from an equation g=Bz=Hf+n (whereinB, H are bi-linear filters, n is a noise component generated by anassumed H when the H is a PSF (Point Spread Function), f is a requestedhigh resolution image, z is a low resolution image, and g is a highresolution image gotten by the bi-linear interpolation method); findinga PSF(P) of a f=Pg function after finding the PSF(H) from the definedadded function M(f); and restoring the requested high resolution image fby finding an added filter coefficient Q of the PSF(P) and interpolationfilter B from the equation f=Pg=PBZ=Qz; wherein the added function M(f)is defined as M(f)=∥g−Hf∥²+α∥Cf∥², wherein α is a regularizationparameter, and C is a two-dimensional high frequency filter for findingthe mitigation of the original image.
 8. The filtering control methodfor improving the image quality a of the bi-linear interpolated imageaccording to claim 7, wherein the regularization parameter α is fixed as‘1’ in order to reduce a computational complexity.
 9. The filteringcontrol method for improving image quality of the bi-linear interpolatedimage according to claim 7, wherein a two-dimensional gaussian filter isused as the two-dimensional high frequency filter C in order todetermine the mitigation of the original image.
 10. A filtering controlmethod for improving the image quality of a bi-linear interpolated imagewhen recovering a high resolution image from a low resolution image, themethod comprising performing operations using at least one processor theoperations comprising: defining an added function M(f) for finding aPSF(H) from an equation g=Bz=Hf+n (wherein B, H are bi-linear filters, nis a noise component generated by an assumed H when the H is a PSF(Point Spread Function), f is a requested high resolution image, z is alow resolution image, and g is a high resolution image gotten by thebi-linear interpolation method); finding a PSF(P) of a f=Pg functionafter finding the PSF(H) from the defined added function M(f); andrestoring the requested high resolution image f by finding an addedfilter coefficient Q of the PSF(P) and interpolation filter B from theequation f=Pg=PBZ=Qz; wherein the PSF(H) is found by an equationH(k,l)=(G(k,l)/F(−k,l),  wherein G(k,l) is the component in the k,lfrequency region of the bi-linear interpolated image, and F(k,l) is thecomponent in the k,l frequency region of the high resolution image. 11.A filtering control method for improving the image quality of abi-linear interpolated image when recovering a high resolution imagefrom a low resolution image, the method comprising performing operationsusing at least one processor, the operations comprising: defining anadded function M(f) for finding a PSF(H) from an equation g=Bz=Hf+n(wherein B, H are bi-linear filters, n is a noise component generated byan assumed H when the H is a PSF (Point Spread Function), f is arequested high resolution image, z is a low resolution image, and g is ahigh resolution image gotten by the bi-linear interpolation method);finding a PSF(P) of a f=Pg function after finding the PSF(H) from thedefined added function M(f); and restoring the requested high resolutionimage f by finding an added filter coefficient Q of the PSF(P) andinterpolation filter B from the equation f=Pg=PBz=Qz; wherein the PSF(P)is found by using an IFT (Inverse Fourier Transform) by an equation${P\left( {k.\mspace{14mu} l} \right)} = \frac{H*\left( {k.\mspace{14mu} l} \right)}{{H*\left( {k.\mspace{14mu} l} \right){H\left( {k.\mspace{14mu} l} \right)}} + {C*\left( {k.\mspace{14mu} l} \right){C\left( {k.\mspace{14mu} l} \right)}}}$H(k,l) is a component in the k,l frequency region of the PSF(H), and Cis a two-dimensional high frequency filter.
 12. The filtering controlmethod for improving the image quality of the bi-linear interpolatedimage according to claim 11, wherein the number of a kernal of thePSF(P) is differently set in accordance with an up-sampling value of theimage.
 13. A method for generating an interpolated pixel data, themethod comprising generating a set of the interpolated pixel data from aset of original pixel data from an original image, wherein interpolatedpixel data for a particular pixel is generated by performing operationsusing at least one processor, the operations comprising: selectingoriginal pixel data for more than three pixels of the original image;obtaining at least a first filter coefficient and a second filtercoefficient, the first filter coefficient and the second filtercoefficient being configured to interpolate the original pixel data;applying the first filter coefficient to the selected original pixeldata to produce first interpolated pixel data, the first filtercoefficient including weighting factors having at least three differentnumerical values, wherein applying the first filter coefficient to theselected original pixel data comprises: multiplying each of theweighting factors and the selected original pixel data to produceweighted pixel data, and summing the weighted pixel data to produce thefirst interpolated pixel data; multiplying the second filter coefficientand the first interpolated pixel data to produce second interpolatedpixel data; and identifying the interpolated pixel data as the secondinterpolated pixel data.
 14. The method of claim 13, wherein the secondfilter coefficient is a matrix that includes one or more individualnumeric values.
 15. The method of claim 13, wherein the first filtercoefficient and the second filter coefficient each comprise at least oneinteger value.
 16. The method of claim 13, wherein a value of the firstfilter coefficient and a value of the second filter coefficient are one.17. The method of claim 13, wherein a value of the second filtercoefficient is one.
 18. The method of claim 13, wherein the originalimage is obtained from a low-resolution imaging system.
 19. The methodof claim 13, wherein the second filter coefficient is a point spreadfunction (P) and the first filter coefficient is a bi-linearinterpolation filter (B).
 20. A method for a moving picture compressionwith a video system by generating an interpolated pixel data, the methodcomprising: generating a set of interpolated pixel data from a set oforiginal pixel data from an original image; and finding a sub-pixelmotion vector using the set of interpolated pixel data, whereininterpolated pixel data for a particular pixel is generated byperforming operations using the video system, the operations comprising:selecting, by the video system, original pixel data including more thanthree pixels of the original image; obtaining, by the video system, atleast a first filter coefficient and a second filter coefficient, thefirst filter coefficient and the second filter coefficient beingconfigured to interpolate the original pixel data; applying, by thevideo system, the first filter coefficient to the selected originalpixel data to produce first interpolated pixel data, the first filtercoefficient including weighting factors having at least three differentnumerical values, the at least three different numerical valuesincluding at least one positive integer value and at least one negativeinteger value, wherein said applying the first filter coefficient to theselected original pixel data comprises: multiplying each of theweighting factors and the selected original pixel data to produceweighted pixel data, and summing the weighted pixel data to produce thefirst interpolated pixel data; multiplying, by the video system, thesecond filter coefficient and the first interpolated pixel data toproduce second interpolated pixel data; and identifying, by the videosystem, the interpolated pixel data for the particular pixel as thesecond interpolated pixel data.
 21. The method of claim 20, wherein thesecond filter coefficient is a matrix that includes one or moreindividual numeric values.
 22. The method of claim 20, wherein thesecond filter coefficient includes at least one integer value.
 23. Themethod of claim 20, wherein a value of the first filter coefficient anda value of the second filter coefficient are one.
 24. The method ofclaim 20, wherein a value of the second filter coefficient is one. 25.The method of claim 20, wherein the original image is obtained from alow-resolution imaging system.
 26. The method of claim 20, wherein thesecond filter coefficient is a point spread function (P) and the firstfilter coefficient is a bi-linear interpolation filter (B).